Four basic operations of arithmetic

We cannot live a day without numerals. Numbers and numerals are everywhere. The numbers used in our numeration system are called digits. In our Hindu-Arabic system we use only ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 to represent any number. We use the same ten digits over and over again in a place-value system. The base of this system is ten.

The digits may be used in various combinations to make different numbers 123, 321, 231 and so on. One and the same number can be represented in various ways. For example, take 8. It can be represented as the sum of 3 and 5, the difference between 10 and 2, the quotient of 80 and 10 and the product of 2 and 4. For example 2 multiplied by 4 equals 8. This is an equation. An equation is a mathematical sentence that has a sign of equality between the numerals. Equations consist of digits and symbols like plus or minus.

There are four basic operations of arithmetic. They are addition, subtraction, multiplication and division. In arithmetic an operation is a way of transforming two numbers into one number.

An equation 2+3=5 represents an operation of addition. Here 2 is an addend, 3 is a summand. Addend is a number to which we add. Summand is a number which we add to. When we add 2 to 3 we get a sum. It is 5.

An equation 5 – 3=2 represents an operation of subtraction. Here 5 is a minuend, 3 is a subtrahend. Minuend is a number from which we subtract. Subtrahend is a number which we subtract. When we subtract 3 from 5 we get 2 as a result. It is difference. Addition and subtraction are inverse operations because we can check addition by subtraction.

An equation 3x2=6 represents an operation of multiplication. Here 3 is a multiplicand, 2 is a multiplier. Multiplicand is a number which is multiplied. Multiplier is a number by which we multiply. When we multiply 3 by 2 we get a result 6. It is a product.

An equation 6:3=2 represents an operation of division. Here 6 is a dividend, 3 is a divisor. Dividend is a number which is divided. Divisor is a number by which we divide. When we divide 6 by 3 we get 2 as a result. It is a quotient. When me divide 10 by 3 we will get a part of a dividend left over. This part is called a remainder and in this case it is 1. Multiplication and division are inverse operations, so we can check division by multiplication and vice versa.

There are two important facts that we must remember about division:

1. The quotient is 0 whenever the dividend is 0. That is 0 divided by n is equal to 0 for all values of n except 0.

2. Division by 0 is impossible.

Task 6

Fill in the chart:

Arithmetic operation	Operation sign	1st member	2nd member	Result
		minuend
				sum
	multiplication sign
division

Task 7

Fill in the gaps with an appropriate word given in the list below:

1. In 3x=12 the … is not known.

2. Today people cannot live without … .

3. "-" is a symbol used in the operation of … .

4. The result of division is called … .

5. We get a product as the result of … .

6. In Hindu-Arabic numeration system we use 10 … .

7. When an equal sign is replaced by a non-equal sign, the … meaning is implied.

8. A mathematical sentence that is either true or false but not both at the same time is called a … sentence.

9. In some mathematical proofs it is … that you write false sentences.

10. The symbol of subtraction is … .

11. You can not … division by subtraction.

12. … by zero is meaningless.

13. When we … two numbers we get a sum.

14. A way of thinking of two numbers and getting one number as a result is a …

15. A … is a a part of a dividend left over.

16. The symbol of addition is called … .

17. A mathematical sentence that has a sign of equality between the numerals is called a … .

18. Addition and subtraction are … .

19. A result of subtraction is called … .

20. The number which is divided by is a … .

21. The number which is subtracted is a … .

add divide inverse operations branches mathematical operation difference check opposite

divisor subtrahend minus equation remainder digits division closed

addition multiplier essential numerals multiplicand plus subtraction quotient multiplication

Task 8

Give definition to the given words. Make use of the example.

e.g. Sum is the result of addition.

addend minuend subtrahend difference multiplicand

multiplier dividend divisor quotient product

Task 9

Answer the questions on the text. Then use the questions as a plan for retelling the text.

1. Why do we need numbers and numerals?

2. What is the difference between a number and a digit?

3. What numerals do we use in our place-value system?

4. What is the base of this system?

5. How can each number be represented?

6. What is an equation?

7. What does every equation consist of?

8. What is an arithmetic operation?

9. How many arithmetic operations do you know?

10. What can you tell about each one?

Task 10

Work in pairs: one of you is a Math teacher, another is a student. The student is being examined. The teacher should assess him or her using one of the questionnaires given below. Dramatize the dialogue in class.

Addition

1. What operation do we make when we add two numbers?

2. What sign do we use in this operation?

3. What is an addend?

4. What is a summand?

5. What is an inverse operation to addition?

6. Why is it an inverse operation to addition?

Subtraction

1. What operation do we make when we subtract?

2. What sign do we use in this operation?

3. What is a minuend?

4. What is a subtrahend?

5. What is an inverse operation to subtraction?

6. Why is it an inverse operation to subtraction?

Multiplication

1. What operation do we make when we multiply two numbers?

2. What sign do we use in this operation?

3. What is a multiplicand?

4. What is a multiplier?

5. What is an inverse operation to multiplication?

6. Why is it an inverse operation to multiplication?

Division

1. What operation do we make when we divide?

2. What sign do we use in this operation?

3. What is a dividend?

4. What is a divisor?

5. What is an inverse operation to division?

6. Why is it an inverse operation to division?

7. What important facts should we remember about division?

Task 11

Read the text and say if addition is a binary operation